Solving for coefficients...

MathGroup:
I am having difficulty getting Solve[] to deal with the following
problem:
m = c1 A + c2 B + c3 C ...
Where A, B, C etc. are known real numbers accurate to 4 decimal places
and c1, c2, c3 etc. are positive integers (0 included). I can measure
m to within 10 parts per million error, I would then like to solve for
the coefficients.
The two problems I see immediatly are 1) the coefficients can only be a
positive integer or 0. To deal with this I have tried including in the
body of Solve[] c1 >= 0 and IntegerQ[c1] == True. The other problem is
that there is error in my measurement, I have tried to deal with this
by putting the above equation into solve as two equations m >= 100.01,
m <= 100.00, for example.
Obviously this strategy has not worked. Any suggestions as to how to
approach this problem using Mathematica would be greatly appreciated.
Should any one care about the application, these are mass spectrometry
data for which I am trying to solve for consistent chemical formulae.
Thanks.
Rob Smith
Department of Biophysics & Biophysical Chemistry Johns Hopkins
University School of Medicine 725 N. Wolfe St.
Baltimore, MD 21205-2185 (410) 955-8712